Wasn't the King married to starks sister and she was murdered? Or have I got that wrong?

In love and going to be married. She was killed by the previous king to Robert who they have called the mad king a few times already, which there will be a lot more on later to learn more about it.

Something else they didn't cover in the book that was early on was that Ned and Robert were raised essentially as brothers as wards to Jon Arryn. They were further linked with the relationship of the mentioned relationship above, which would have also linked two strong houses of Stark and Baratheon.